Inside cell nuclei, DNA is stored in the form of chromatin. Chromatin is three-dimensionally organized in response to transcription of DNA into RNA. Here, we studied the mechanisms by which transcription organizes chromatin, using experiments in zebrafish embryonic cells and theory. We show that transcription establishes an interspersed pattern of mutually exclusive chromatin-rich domains and RNA-rich domains. Ongoing transcriptional activity stabilizes the interspersed domain pattern by establishing contacts between the RNA and transcribed parts of chromatin. We explain our observations with an active microemulsion model based on two macromolecular mechanisms: (i) RNA/RNA-binding protein complexes and chromatin undergo phase separation, while (ii) transcription tethers RNA/RNA-binding proteins to chromatin and thereby forms amphiphile particles that intersperse the phases. Thus, three-dimensional DNA organization in the cell nucleus is an example of an unconventional, active microemulsion, stabilized by a catalytically active amphiphile that produces one of the emulsified phases.